Let AB be the chord passing through the center of the ellipse and f be a focal point of the ellipse? The ellipse is x ^ 2 + 2Y ^ 2 = 1
I think we should find the maximum area of triangle ABF, LZ may be wrong
Let a (x1, Y1), B (X2, Y2)
According to the meaning of the title, | Y1 | = | Y2 |, and Y1 and Y2 are opposite numbers
Of length is constant, s = 1 / 2 * of * | y1-y2|
So when | y1-y2 | is the largest, s is the largest
Draw a picture to see that when AB is the endpoint of the minor axis respectively, | y1-y2 | is the largest
Then | y1-y2 | = 2B = radical 2
Of = C = radical 2 / 2
S = 1 / 2 * radical 2 * radical 2 / 2 = 1 / 2
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